The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is

Step-by-step solution

There are 5 vowels in the given word which are 4 E ' s   &   1 I . Since they have to always occur together we take them as a single object E   E   E   E   I for the time being. This single object together with 7 remaining object will account for 8 objects. There 8 objects in which there are 3 N ' s   &   2 D ' s can be arrangement in 8 ! 3 ! 2 ! ways. Corresponding to each of their arrangements the 5 vowels E , E , E , E   &   I which can be a